Evolution of cooperation in Axelrod tournament using cellular automata

Results of the Axelrod Tournament were published in 1981, and since then, evolutionary game theory emerged as an idea for understanding relations, like conflict and cooperation, between rational decision-makers. Robert Axelrod organized it as a round-robin tournament where strategies for iterated Prisoner’s Dilemma were faced in a sequence of two players game. Here, we attempt to simulate the strategies submitted to the tournament in a multi-agent context, where individuals play a two-player game with their neighbors. Each individual has one of the strategies, and it plays the Prisoner’s Dilemma with its neighbors. According to actions chosen (cooperate or defect), points of life are subtracted from their profiles. When an individual dies, some fitness functions are defined to choose the most successful strategy which the new individual will copy. Although tit-for-tat was the best strategy, on average, in the tournament, in our evolutionary multi-agent context, it has not been successful.

[1]  V. M. Ghete,et al.  Observation of the Associated Production of a Single Top Quark and a W Boson in pp Collisions at √s=8 TeV , 2014, 1401.2942.

[2]  B. Sinervo,et al.  The rock–paper–scissors game and the evolution of alternative male strategies , 1996, Nature.

[3]  D. H. Zanette,et al.  Synchronization of multi-phase oscillators: an Axelrod-inspired model , 2009 .

[4]  Jinhu Lü,et al.  Characterizing the effect of population heterogeneity on evolutionary dynamics on complex networks , 2014, Scientific Reports.

[5]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[6]  Samuel Rota Bulò,et al.  Infection and immunization: A new class of evolutionary game dynamics , 2011, Games Econ. Behav..

[7]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[8]  Kai P. Spiekermann Sort out your neighbourhood , 2009, Synthese.

[9]  G. S. van Doorn,et al.  Coaction versus reciprocity in continuous-time models of cooperation. , 2014, Journal of theoretical biology.

[10]  Punishment Strategies in Repeated Games: Evidence from Experimental Markets , 2010 .

[11]  Ariel Fernández,et al.  Prisoner’s Dilemma cellular automata revisited: evolution of cooperation under environmental pressure , 2005, physics/0512187.

[12]  Syi Hidden patterns of reciprocity. , 2014, Journal of theoretical biology.

[13]  Zhongke Gao,et al.  Spatial prisoner's dilemma games with increasing neighborhood size and individual diversity on two interdependent lattices , 2015 .

[14]  D. Keltner,et al.  When the selfish suffer: evidence for selective prosocial emotional and physiological responses to suffering egoists☆ , 2014 .

[15]  R. Axelrod More Effective Choice in the Prisoner's Dilemma , 1980 .

[16]  Martin A. Nowak,et al.  Punishment Does Not Promote Cooperation Under Exploration Dynamics When Anti-Social Punishment Is Possible , 2014 .

[17]  Long Wang,et al.  Emergence of parochial altruism in well-mixed populations , 2015 .

[18]  P. Grim,et al.  Spatialization and greater generosity in the stochastic Prisoner's Dilemma. , 1996, Bio Systems.

[19]  P. Grim The greater generosity of the spatialized prisoner’s dilemma , 1995 .

[20]  Paul E. Turner,et al.  Prisoner's dilemma in an RNA virus , 1999, Nature.

[21]  Attila Szolnoki,et al.  Interdependent network reciprocity in evolutionary games , 2013, Scientific Reports.

[22]  M. Nowak,et al.  Evolutionary Dynamics of Biological Games , 2004, Science.

[23]  R. Axelrod Effective Choice in the Prisoner's Dilemma , 1980 .

[24]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[25]  Jie Liu,et al.  Evolutionary behavior of generalized zero-determinant strategies in iterated prisoner’s dilemma , 2015 .

[26]  Maxi San Miguel,et al.  Is the Voter Model a model for voters? , 2013, Physical review letters.

[27]  D. Stephens,et al.  The economic basis of cooperation: tradeoffs between selfishness and generosity , 2004 .

[28]  Xingyuan Wang,et al.  Robustness of cooperation in memory-based prisoner’s dilemma game on a square lattice , 2014 .

[29]  Jun Tanimoto,et al.  Impact of deterministic and stochastic updates on network reciprocity in the prisoner's dilemma game. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Jun Tanimoto,et al.  Relationship between dilemma occurrence and the existence of a weakly dominant strategy in a two-player symmetric game , 2007, Biosyst..

[31]  J. Busemeyer,et al.  Understanding cooperation in the Prisoner’s Dilemma game , 2011 .

[32]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[33]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[34]  U Motro,et al.  Co-operation and defection: playing the field and the ESS. , 1991, Journal of theoretical biology.

[35]  Ronald Noë Cooperation experiments: coordination through communication versus acting apart together , 2006, Animal Behaviour.

[36]  Alewyn P. Burger,et al.  An asymptotic analysis of the evolutionary spatial prisoner's dilemma on a path , 2012, Discret. Appl. Math..

[37]  P. Schimit,et al.  On exploring the genetic algorithm for modeling the evolution of cooperation in a population , 2014, Commun. Nonlinear Sci. Numer. Simul..

[38]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[39]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[40]  Patrick Grim,et al.  A graphic measure for game-theoretic robustness , 2008, Synthese.

[41]  Tim Clutton-Brock,et al.  Cooperation between non-kin in animal societies , 2009, Nature.

[42]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[43]  S. Pinker The Better Angels of Our Nature: Why Violence Has Declined , 2011 .

[44]  Maxi San Miguel,et al.  Erratum: Is the Voter Model a Model for Voters? , 2014 .

[45]  Robert Forsythe,et al.  COMMUNICATION IN THE BATTLE OF THE SEXES GAME , 1989 .

[46]  D. Jackson Spatial pattern as an adaptive phenotype , 2014 .

[47]  Long Wang,et al.  Time scales in evolutionary game on adaptive networks , 2014 .

[48]  C. Cannings,et al.  The Generalized War of Attrition , 1997 .